Two- or three-stage least squares?

Two elements enter the choice between 2 and 3SLS for full-system estimation: statistical efficiency and computational cost. 2SLS always has the computational edge, but 3SLS can be more efficient, a relative advantage that increases with the strength of the interrelations among the error terms. A measure of these interrelations is thus helpful in making the choice, and, when there are only two equations, this has suggested using a high pairwise error correlation as an indicator of when to use 3SLS. In larger systems of equations, however, these pairwise correlations can remain small even though more general interrelations give 3SLS the relative advantage. More general indicators are therefore needed, and this paper suggests three such and demonstrates their efficacy.Professor of Economics, Boston College, and Principal Research Associate, Center for Computational Research in Economics and Management Science, MIT. All computation was done on the TROLL system at MIT. My thanks go to Josh Charap for his able research assistance. This research was sponsored in part by the National Science Foundation under grant #IST-8420614.     

Push-pull bithiophene azo-chromophores bearing thiazole and benzothiazole acceptor moieties: Synthesis and evaluation of their redox and nonlinear optical properties

Three series of bithiophene azo dyes functionalized with thiazol-2-yl or benzothiazol-2-yl-diazene acceptor moieties were synthesized through azo coupling reaction using 2,2′-bithiophene, 5-alkoxy-2,2′-bithiophenes, 5-N,N-dialkylamino-2,2′-bithiophenes and thiazolyl- and benzothiazolyl diazonium salts as coupling components. The 5-alkoxy-2,2′-bithiophene precursors yielded the 5-thiazolylazo-5′-alkoxy-2,2′-bithiophenes, while the azo coupling reaction of 5-N,N-dialkylamino-2,2′-bithiophenes with the thiazolyl diazonium salt gave 4-thiazolyl-azo-5-N,N-dialkylamino-2,2′-bithiophenes. A different reactivity behavior was observed for 2,2-bithiophene with thiazolyl diazonium salts which gave rise to the expected azo dyes together with several arylation products. The redox behavior, thermal stability, and the first hyperpolarizability of the novel chromophores were evaluated through cyclic voltammetry, thermogravimetric analysis (TGA) and hyper-Rayleigh scattering (HRS) respectively. By varying the position of the thiazolyldiazene acceptor group on the bithiophene system, the electrochemical behavior as well as the optical (linear and nonlinear) properties of the donor-acceptor π-conjugated systems can readily be tuned. Push-pull 5-thiazolylazo-5′-alkoxy-2,2′-bithiophenes exhibit the most promising redox and the solvatochromic properties and second-order nonlinear optical response. The redox and the optical properties also show notable variations for the different heterocyclic spacers and were also sensitive to the electronic acceptor strength of the (benzo)thiazolyldiazene moieties.     

Synthesis and optical properties of novel, thermally stable phenanthrolines bearing an arylthienyl-imidazo conjugation pathway

Six new hyperpolarizable chromophores based on functionalized arylthiophene donors and an imidazo-phenanthroline acceptor moiety have been designed and synthesized for the first time in good to excellent yields by condensation of 5,6-phenantroline-dione with formyl-arylthiophene derivatives in the presence of ammonium acetate in glacial acetic acid. The thermal stability, solvatochromic and nonlinear optical properties of these compounds were evaluated.     

The synthesis and characterization of heterocyclic azo dyes derived from 5-N,N-dialkylamino-2,2′-bithiophene couplers

Heterocyclic azo dyes were synthesized by diazotation of several substituted anilines and coupling with 5-N,N-dialkylamino-2,2′-bithiophenes to give 4-phenylazo-5-N,N-dialkylamino-2,2′-bithiophenes. This reaction contrasts with the behavior of 5-alkoxy-2,2′-bithiophenes towards aryldiazonium salts which provides 5-phenylazo-5-alkoxy-2,2′-bithiophenes. The thermal stability of the derivatives was evaluated using thermogravimetric analysis and their solvatochromic behaviour was investigated in several solvents of different polarity. The experimental results indicate that the heterocyclic azo dyes could be used as thermally stable, solvatochromic probes.